## College Algebra (10th Edition)

The solution set is $\left\{0, 9\right\}$.
Square both sides to obtain: $x^2=(3\sqrt{x})^2$ Use the rule $(ab)^m = a^mb^m$ to obtain: $x^2=3^2(\sqrt{x})^2 \\x^2=9x$ Subtract $9x$ on both sides of the equation to obtain: $x^2-9x=9x-9x \\x^2-9x=0$ Factor out $x$ to obtain: $x(x-9) = 0$ Equate each factor to zero, and then solve each equation to obtain: $\begin{array}{ccc} &x=0 &\text{ or } &x-9=0 \\&x=0 &\text{ or } &x=9 \end{array}$ Thus, the solution set is $\left\{0, 9\right\}$.